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 A268216 Triangle read by rows: T(n,k) (n>=2, k=3..n+1) is the number of topologies t on n points having exactly k open sets such that t contains exactly one open set of size m for each m in {0,1,2,...,s,n} where s is the size of the largest proper open set in t. 7
 2, 3, 6, 4, 12, 24, 5, 20, 60, 120, 6, 30, 120, 360, 720, 7, 42, 240, 840, 2520, 5040, 8, 56, 336, 1680, 6720, 20160, 40320, 9, 72, 504, 3024, 15120, 60480, 181440, 362880, 10, 90, 720, 5040, 30240, 151200, 604800, 1814400, 3628800 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 2,1 LINKS G. A. Kamel, Partial Chain Topologies on Finite Sets, Computational and Applied Mathematics Journal. Vol. 1, No. 4, 2015, pp. 174-179. EXAMPLE Triangle begins: 2; 3, 6; 4, 12, 24; 5, 20, 60, 120; 6, 30, 120, 360, 720; 7, 42, 240, 840, 2520, 5040; 8, 56, 336, 1680, 6720, 20160, 40320; 9, 72, 504, 3024, 15120, 60480, 181440, 362880; 10, 90, 720, 5040, 30240, 151200, 604800, 1814400, 3628800; ... MATHEMATICA i = 1; Table[Table[Binomial[n, i] FactorialPower[n - i, k], {k, 0, n - i - 1}], {n, 2, 9}] // Grid (* Geoffrey Critzer, Feb 19 2017 *) CROSSREFS Row sums give A038156. A008279 (main entry). Triangles in this series: A268216, A268217, A268221, A268222, A268223. Cf. A282507. Sequence in context: A097275 A130879 A119741 * A346928 A245712 A285331 Adjacent sequences: A268213 A268214 A268215 * A268217 A268218 A268219 KEYWORD nonn,tabl AUTHOR N. J. A. Sloane, Jan 29 2016 EXTENSIONS Definition clarified by Geoffrey Critzer, Feb 19 2017 STATUS approved

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Last modified March 28 03:48 EDT 2023. Contains 361577 sequences. (Running on oeis4.)